Đáp án:
\(\left[ \begin{array}{l}
x = \frac{8}{5}\\
x = \frac{7}{2}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ {2;4} \right\}\\
\frac{{x - 3}}{{x - 2}} - \frac{{x - 2}}{{x - 4}} = \frac{{10}}{3}\\
\to \frac{{3\left( {{x^2} - 7x + 12} \right) - 3\left( {{x^2} - 4x + 4} \right)}}{{3\left( {x - 2} \right)\left( {x - 4} \right)}} = \frac{{10\left( {{x^2} - 6x + 8} \right)}}{{3\left( {x - 2} \right)\left( {x - 4} \right)}}\\
\to 3{x^2} - 21x + 36 - 3{x^2} + 12x - 12 = 10{x^2} - 60x + 80\\
\to 10{x^2} - 51x + 56 = 0\\
\to 10{x^2} - 16x - 35x + 56 = 0\\
\to 2x\left( {5x - 8} \right) - 7\left( {5x - 8} \right) = 0\\
\to \left[ \begin{array}{l}
5x - 8 = 0\\
2x - 7 = 0
\end{array} \right. \to \left[ \begin{array}{l}
x = \frac{8}{5}\\
x = \frac{7}{2}
\end{array} \right.\left( {TM} \right)
\end{array}\)
